Antenna array



Aug. 15, 1933. J. s. STONE 1,922,115

ANTENNA ARRAY Filed April 12, 1930 5 Sheets-Sheet l 20 40' 627 ab" .9 zoo v 12a ATTORNEY Aug' 15, 1933- J. s. STONE 1,922,115

ANTENNA ARRAY Filed April 12, 1930 S'ShetS-Sheet 2 C f EL' ./0 Il? 4l i *d* z* T l 7 2 2 07"' 2- o'r 07T l i i l ITF 5+# {2y/iw TTORNEY Aug. 15, 1933. J. s. s'roNE 1,922,115

ANTENNA ARRAY Filed April 12, 195o s sheets-'sheet 4 1.0'

l I l I l l l L l I i 27 @-l ly INVENToR @luz Stm/Le Zane ATTORN EY Aug. 15,1933. J. s. sToNE 1,922,115

ANTENNA ARRAY Filed April 12, 1930 5 SheebS-Sheet 5 convo Earthly Sagface 2.6- .sfsmr Earthfs .Surface 000 4l 1' C 1 2,2 Ea/*tha* Suf/ace 6.800 4.24 0

Jigl/b Stof/be Sto/foe ATTORNEY 25- claims.

t srArss Arsnr orricg y ANTENNA ARRAY .lohn Stone Stone,` San Diego, Calif., assigner to American Telephoneand Telegraph Company, a Corporation ofk New YorkV Application April 12, 1930. serialrNo. 443,830 9 Claims. (ci. 25o-33) The principal object of my invention is to provide an'ew and improved antenna array 'for the transmission or reception of radio communication waves. Another object is to provide a meth- 5 od for directionally selective transmissionor reV` ception of such waves. Another object is to provide lfor directional Vselectivity with suppression of'beamsoftransmission or receptivity in particular undesired directions. Other objects l0 have to do with securing the advantages of directional selectivity by means of antenna arrays of limited extent; distributing the power to the antennas ofA an array' (or receiving the power therefrom) so as-to coordinate their operation;

f l5 anddirecting a beam of radiation at any suitable desired anglerelatively tothe axis of the array. All these objects and other objects of my ihvention willY become apparenteon consideration of a limited number of examples of practice of the 20 invention which `-arejpresented in vtheffollowing speciiication'. It willbe understood that this dis closure Vrelates to these particular examples of the invention and that the scope of the inventionis intended to be indicated in theappended Referring to thedrawings,Figure 1 is a plan Vdiagram iliustrating an array tapered to-form what I call a parabolic image array; Fig. 2A is afplan diagram of an array similarly tapered .30. but ina manner differing in detail from Fig. 1;

' Fig.'3 4isaplan diagram for a parabolic array with its power supply lines; Fig. 4 is a lplan l' y diagram or an'array equivalent in its effect 1 at a distance to the array of Fig. 3; Fig. k571s 'a plan diagram of what kI call a binomial law array with a maximum of intensity in a direction transverse tothe extent of the array; Fig. Y rGis a diagram of 'asimilar array but with the maximum longitudinal to the' extent of the array; Fig. 'lis ae'plan diagram of a two-dimensional or vrectangular binomial law array; Fig. 8 is. a'curve diagram giving a comparison of ref sults from curtailed and non-curtailed tapered o' tain antenna couplet employed in Vsome embodiments of my invention; Fig. l() is a diagram: showing an array obtained by substitution of theV couplet of Fig. 9 for each of the units of Fig. 1; o Figs. 1l and 11a are plan diagrams for a triplet anda quadruplet, respectively, of properties sim- 755, bani'r'of radiationrFig. 13 is 'a similar diagraml arrays; Fig. 9 is a cardioid diagram f or acer-- for a longitudinalbeam; Figs. .14 .and 15 are` diagrams illustrating power distribution tothe antennas of an array in sequencein a network; Figs. 16, 17, 18 and 19 are further diagrams similar to Figs. 14 and 15; Figs. 20, .21, 22 and 60 23 are diagrams showing conductive connections between antennas to neutralize theirinterac tion through space; Fig. -24 is a diagram for phase relations for an oblique beam of transmission by analogy to reection of lightfrom a 65* plane mirror; Fig. 25 is a diagram of a binomial law array with the antennas energized in proper phase relation to give an oblique beam; Fig. 26

-is a curve diagram showing the intensity ,of radi- Heaviside layer; Fig. 3151s a diagram illus- 80 I trating an array disposed-and adapted for send-` ing a` beam in an upwardly Vinclined direction relatively -to the earths surface; Fig. 32fis a diagrammaticv elevation of an array with its axis of extent tilted in order to secure a tilted beam 8 5* of radiation transverse thereto; Fig. 33 is asimilardiagramv except `that in this case the beam is longitudinal lto theextent of the array; Fig. 34 isa diagrammatic elevation of a` horizontal array with which an upwardly inclined beam' is 9.0

secured-by establishing suitable phase relations among the antennas; `and Fig.' 35 isa similar diagram except that the'extent of the array is Vertical instead of horizontal. Y

. i For convenience and. deiniteness of exposition, 95 n I shall confine thevfollowing description to'antennas used fortransmitting.. Itis well` undere stood that to a greatextentthe principles of` directional selectivity for transmission are' ap- 00 plicablesimilarly for reception and this will ybe readily appreciatedY in the present connection. Referring to Fig. 1, this shows a. straight-line array of equally spaced antennas separated the interval d,rwhere d/li. These antennas 105 are intended'to be operated all in the same phase andat intensities given by the lawg` 1=4a/ 4a2+'y2 w' where a is a constant and yis the distance `from 110 the center of the array tothe 'particular antenna v.

Then the intensity .of the radiationin any 4drec--- 'gOng disclosure QODDeCKtOn therewith hOW t0 g Y,

. tion given bythe .gnglexib is v l f cmstruct andlenergize a lineararray;according` u j Y Y rf l to the samerprinci'ple for any' number-offan-A l mind y v f mcl2 i {'vIn thelinearantennafarrays.that 'havefbeen *Ig Y '5&6705( V2 90W/@+ 4 '(2) discussed thusiargihefjdirciion i' maximum 'n1- 1 f vtransmission is transverse Ito "therextent ofv the 1 v' in Fig. 1,-th'eylV maybev spaced y,nnequ'ally asyin' .l

for which the `formulan is, employed.' In the pres- VVentr example I'assume that the number of ane 1 f l `tennasl is an even number.' YIt ,Willvre'adilyfbe- Y seenhow to extend the principles here presented toranlodd number` Let this even number leen.Y

Instead'of spacing the antennas equally" Fig. 2, Y'r'naking therdensity of theirv spacin`gac-1 cordingto thev proportion .given byFOrmula (1);,

. and energizing l the'y individual, antennas alike.

ble forit is based on. a uniform. interval Where Qi tal Iii-V yIn thiscase dsta'nds forel.'`

i In a'rrnodiflcation' of the parabolic Yin iage, ar-.

" ray, the individual antennas may be distributedf otherwise ythan a straight 'line,:in-fwhichcase lthey'will not, in generalgvbeener'gized allinflthe straight lines,` respectively; to the antenna.

. Vwin be inline direction 'ofthe Fv andy 'they are =energized.` 1by;conductors that go.; from central station It to .l F andi.thencel "along It direction oppositer thereto.;

y, Theantennas Ydonot need ,tof lie-located vonora 1 parabola, butv may.; be scattered irregularly asV shown at L1a,.2a, Ae.tc;,in Fig- 41 Herethe elec! properlyfbe made .equal4 vto ftheifcorresponding raymay-.betaperedwith'fsmilareffect accordingy trical lengths of the respectiue conductors may l The foregoingdiscussionrelatesytolineartm pereii4 parabolicV image1. arraysi YBut ajlinea'r ar- A' to a 1aw which I can fthe,binomiai law because f integer. I'hus, 9 for exarrnplV of Yitsanalogy. to` thev coeflicients in tl'ie-eiqiansioni @fea Abinomial ma powerf'givenfby 'a @Sivit/.ef

A in j the plan gy 5,

',ygaveleng'lth. In tidearraysnownjin Fig.' there. .l are '7 antennas., Thefbinonnal expansion vto *then-.a direti--trnzsverse tb Ythat `,f deslsed -majx1 1 sixth powergivesse'ven terns and theeoeiloients Offthesel. .Seven terms are; 6, f1.5; 20;'i1j'5y "'r'id 1 f .inl orderiiao'codingly.r these kr'nnriber's represent`r the relativefpower magnitudes -on the respective pl'oyedl later, that theV antenna y'are .energized in thesam phase.

Y 1,922,115 n i .It will readily be seen fromv Fig. `45 and the Y.fore- .two opposite maxina *of -transmissionfintensityi -alcngthe axis vof thefarray; Referring'to Fig.

--etransmissionparei in the .direction of" the Y B1 and B2 and` theinten'rsity'inany direction is 100 Hthe sainenumberfofnnnits whosev axis VVo1', 'exten-g sion is' perpendicular toV the;,beanf1;`onthe other Y v. n Y. h&I1.d,-`such.la;taperedfrectangularyarrayggives Yafhearn Whicli-isiore narrow than Vthat from e120.l .tapered mearl arayoi an yequal number .fof Y fntswhose aXi Tapered Vrectangularf 5 arrays i :giveyradiatiop i. .l 'Y

V125 ,Y ypendi'cular tofeach other, v,'i' r1'stead *of.oneprixr-s.,` i'. double restriction ofthe radiation in Vtheasedf Y tion is 'according to 'thejformula YForjthefarrayofi-.Fig tithe intensity of radia-V thisqs'hows Va Ylinear array of seven antennas A:spaced by `-the ,distance M2 andlenergized rf-ff 95; j YFignn vthey .are noti-inther samegphaseabutmr.-

intensity accordingftothe binomial law.l vBut vin alternately oppositein phase as indicated. by the" syrnbols 0*,ff1r, 21r,Y 31r,' etcj. Here the 0Il 'l givenby l,the form'ula'. Y

Vltetangul'ar arrays'can, loe-built uo-from .inrigenerarjihe meihodgoipiocedureiis maart with Vva linearr'tapered'array and replace each of its funits liya linearlvltapered arrayY lyingf'in transverse directionjiandvaryins thetotal energy. 110,1 'Y ineah-.component linear array :according3.othe I I law Lf or the yinitialflinear array Y whose' A. taperedV rectang row. ,thanthatV from I' a` tapered vlinear iarryvfo which is restricted intwo'v principal .planes cipal *planet as vfor .taperedlinearA arrays. f This l taperedrectangular arrays gives ane'conomy of 1 power in transmission and is'z'oi advantage inthe caseof `receivers throughth'e. diminution of the A `eect fstrays or static. IThe?rectangular Yar-l iayslgiaveithe advantage'fthat theyfperxnit,theyV f Y tivelyfrestricted space/ 1 i u se or. .a `llarge numberoffantennas in a relaa. Y

up'faccordinglto the following plan firstj lineark array. with`th e nnits in the Vsame lphaserenerf gizedaccordingtolthebinomial law'is set upv ini.

'transmission which 'is`V indicatedjbylth,

arrows.BifazidfBa` VThen each unitof linear` 'y arrayis Y'replaced*by alinear array extending n transverselyjthfereto fand -of the .typt-5 fv 'vl'ii chv theA units are not in the sanieaphase', and

"1f-eral lfor such a rectangular array the intensity or Avvw i beam, but. with this slight impairment of direcradiation in any direction in the equatorial plane of the' oscillators will be givenn by the formula From the foreging description showing how lineararrays canbe compounded. into rectangular arrays,.it will readily be seen that one can set up a linear array and replace each unit by a rectangular array and. thus get a threadimensional array. f

' In any of the arrays heretofore considered, linear, rectangularA or.:three-dimensional, it will b e seen that the great bulk of the powerof the Y array lies in the. central units. For example, in

K Fig. 7,: the antennas nearest the center of the array each carry 69 units of energy and those atthe corners each carry only 1 unit. As the result of a study that I have made, I find that some of the marginally located low power units can .be suppressed withV only a negligible impairment of the'directional selectivity, `but with decided reduction of the vphysical extent of the antenna array. For example, in a' simple tapered'linear array of 11 oscillators,` the two end oscillators may be omitted. This omission will introduce a fringe of radiation in a direction transverse' tothe maximum and amounting to vabout 0.2 per centof the-intensityof the main tionalselectivity goes a reduction of 18 per cent.

in the'physical extent of the array. Thus it will be seen that tapered arrays can be very muchsimplied if and. when we can tolerate the Y'presence of fringes AWhose intensities, relatively to that of the main beamof the array, are rather small. The more lextensive-the array, the greater the simplicationwhich can be eiected. Again, 'consider a taperedlinear array of 21 oscillators. This can becut down to 11 oscillators-that is, it can be cut down in physical extent nearly percent-f-and yet the resulting fringes that will appear in directions transverse to the main beam will beless than 1.18 per cent. of that-beam intheir intensity.

Putting the proposition in slightly different ,k lform, Awe limit'ourselves toa certain number oli-junitantennas,l We can get far better direc- .tional selectivity in acurtailed tapered array than. in one not curtailed, provided we are i ,Zwilling vto endure the presence of small transverseffringes. In Fig. 8, the intensity of radiavtion isplotted as a function ofdirection for two arrays of 12 units each. The' least selective diagram (curve No-1) is for a 12-unit` complete 'tapered array. 'Ihe more selective diagram (curve No. 2). is fora 26-unit array whichl by f curtailment,.has been brought down to 12 units.

In the latter case there will be vfringes of less than 13163 per cent. Curve No. 3 is .for a l-unittapered array not curtailed...

A ikt One. advantage ofthe curtailed tapered arrays V'Lis Vth,e..1'eduction in theV disparity of intensity -f along the. antennas. Tlius in a complete array of12 units,1the binomial coefficients range from .1 uplto 462.y But'in an array on the basis of 26iunits `curtailed to 12, the binomial coecients range from 480,790 up to 5,20,300, a ratio. of

1- 4about 135018.'A

1 :In the arrays that. have been considered thus beam of radiationina particular direction can be Asuppressed by substituting for each unit ofi the array a couplet, or other small group, as will now be pointed out more particularly.

Consider the couplet or pair of oscillators each marked 1 in Fig. 9. If these are excited'in equal intensity andin the phase relationfand wave length. relation indicated in theY drawings, they will give a polar diagram of radiation intensity according to .the cardioid curve of `the drawings, and it will be noticed that in one particular direction radiation is nil.. l v Now in any'array such; forexamplaas the array of Fig. 1, if it is desiredl to suppress'a beam .of radiation in a particular direction,

such as the beam B2 of Fig.`1, .then for each unit of Fig. 1 vsubstitute `the couplet of Fig. 9 with its direction of null radiation in the direction or^ desired suppression. This gives Fig. 1G instead of Fig. 1.\Y TheI radiationas a function oi direction in the cquatoriol` plane of the oscillators is'given bythe formula.

The foregoing formula is obtained by .multiply-l ing the formula for Fig. 1 by that for Fig. 9, andthis is Vthe general method.

Instead of the couplet ofv Fig. 9 being substituted for each. unit oscillator lofv an array, the triplet oi Fig. 11 may be substituted or the quadruplet of Fig. 11a.` Each of these aggree gations gives an effect in substitution similarA Theadvantage o f this substitution lies not alone in economizing the radiated energy but in reducing the radiation in directions in which it might be regarded'as. a serious interference with receiving stations lying in those directions.

I have already touched upon the question of distributing the power :to the respective antennas 'of an array; this was in connection with Figs. 3 and e in whichthc powerconductors between Ythe central receiving station R and the various antennas were each given the proper electrical length. Another way to distribute the power with certain advantages will ,now be disclosed.` Suppose, for example, that we have the Vtapered linear array whose eight antenna units are indicated by the numerals 17, 2l, 35, 35, 21, '7 and l in Fig. 12. These antennas may be considered to lie across the axis of a parabolav` whose focus is to be F. Accordingly, power lines connecting F to these antennas will have will readily be appreciated in accordance with the geometrical properties of the parabola. Orf

course, this is only one way, but a very` symmetrical way, of representing the power. circuits. It may be departed from, provided .that the vlengths and phase speeds of the several lseparate.` supply circuits are maintained `the same as here represented. The foregoing disclosure in connection with Fig. 12 is for a case in which the beam of radiationis at a right f angle lto the direction ofextent of the Alinear array.'i.Forva.case in which the beam of radia. tion is along! the direction of extent 'of `the linear array, the distribution -of power.between, the Acentral stationS `'andgthe respectivefan Vtennas .maybeV asy Vshownin Fig. 113. Each liney `from S tojan antenna'unit represents a two-Wire fio circuit.: The'difference between the lengths of the circuits leading to .any two consecutive an# tenna units is equal to; Vthe :distance ,fbetween' them; this is basedon the assumption that the phase'speedin the'supply circuitsdoes not' *diier' materially frornf thejvelocity of j transmis-v sion'in the ether. l f .The power and'phase4distributiontothe an-V tenne.V units may beieffetedwithout the neces? sity of having a separate lead extending,.from

l fthe sourceto each"of.,the voscillators orfantennasv oflthe array. may be eiectedv by making` the antennas part fof la' network so constructed `and connected that -each vrantenna' oscillates 'l Y resonantly' to the centrally impressed -fforce and at the intensity and phase proper toitsfposi [tion in the' array. Injsuch a network the conductors whose functions are merely to distribute power should be non-radiative; this condition will be secured by'disposing them in pairs, the 'members of Yeach pair being close togethery compared to a quarter-.waVe-length and isothat -the poten'-v tialsand currents in the two. conductors of-such a pair shallbe substantially .equal inV intensity andV Voppositein phase, or elsefby arranging thatthe currents and Vpotentials in the distributing con- V ductorsshall be Vof 'such-small magnitude that they dof not give av disturbing radiation. 1Infthe networks according tothe present plan,l

thel'radiative linear oscillators `are, of course.,V

' inv resonance withV the forces impressedon the system, andceitain other parts of the ,networkVv are likewise, in resonance by virtue ofthe'in lengths. `The resonant sections are. marked. 'off'- bytheintroduction of inductance coils, Vat the points ofjcurrent nodes and potential loops. For

Vfexample, in Fig. -14 the linear oscillators are a1` Y ranged end to end and lenergized .from acentral source SL The connectingconductors between {adjacent ends arey of such 'length thatfthe' phase relations'Y are established'V as'indicated in the A. drawings. VThere isa currentz no deand a po-I tential-flooplat each-V of vthe inductances. rl'hc extended linearoscillators are radiative but the A*loop circuits between them are practically non-Y.. radiative in accordance with the principles set-Y yforth above.v f

- It maybe desirable `tor` decrease or *increasev the wave speed in the power supply conductors.

`A reduction of this-speed maybe accomplished. by the use of small,.seriallyconnected in'" here "suggjestedj AYis shown. in

extension ofthe' array. .When the axisY of the vbeam Y- of radiation is coincident Awith the axis of extension of the jarrayja diierent system of distribution lwill be employed :fwhich isV illus- 'are approximately equalv in.. intensit'yfand cip-*LA `the oscillators of anfarrayhas fbeenf' ignored.; 1

au thejotherrosciilatorsofthe array undying.: therefore ,be subject to electromotive forcesother and phasedetermining'arrangements'asprevi- Q -i n' 'mentfmust in 'every instance'. .be empirical. '.ll'iiskV 'r Y Y 'nal adjustment will beinthe 'natureoa corlf" f which vvis easily "dona andiL make vcorrection aci fcordinglyl ,.I'l'i'ef'correctionWillinfall instances A Y consist in a i slight.' lengtheningr'or-f'-shortening l j. f [oil the, elec trical-j lengthjof fa'segmentor f inents ofY the.pwen'andphase distributing .cir-; cuits., It is vto'be.remembered' that the electrical .1115

, additions? ai smaiifinduqcance-at its electrica; j

Another direct .methodjf'or meeting lem presented bythe natural interaction of For examplepsuppose the two. 'of-*Figi Vtime,'re `1uiredi:fcniradiation 'to pass Irom oneI Vto the; other "shallfbeA substantially. "theirjms? 20"'will1becf .the Vtype .propeito suppress'the It isf'hereassumedfthat the wave` speedfi.n=gthe .two-wire circuitA connecting the oscillators 'Y "length'f qfgtheeoupiing circuitv may mistici-tened -the radiationlf'iseither"transverse to fextentpf the arrayA or -longitudinalthereto. It.:y

A.maximum radiationin a-.direction Voblique'lto- 'trated' in Fig. j 19, landt-1in Fig.- v15 -"mentioned("' heretofore.v

In .the systemjshown'in Figs. ,14a`nd 16, likes Wise in Fig. 27,' thesupplyfbranchesf are in them areY too small to produce *effective radiaf tion. .On the otherhand; in the systemsshown infFigsml '1, '118 and VA-19v4 the supply "branches are 4 resonantbut aredisposedin pairs of conductorsrsothat thev currents. and-potentials K,

posite in '.phase, and-.therefore 'they giverise-.to no cpnsiderableradiation1 'llo this point the matter of "interaction among.

Clearly,- fhowever; Yeach ioscillator of anfarrayj will be underthe infiue'nceof Atl'ie`eld forcentV than Athose1 .conveyedto 4it by the Y powerf" phaseV distributing 'circuits.- Unlessv Jwe. Y these interactionslthe adjustment of the power p ou'sly described "canonlybevregardedasa first I approximate adjustment... and 'the` tlnal adjust?. 100

rection ofv thetheoretical adjustment oftpower. and phasepreviouslydescribed. "Ihe interactionof theoscillators of 105 forany; given' intensityandf phasedi'stribution, is, of' course, 'capableiof`V` predeterrnination..- 1' But theEresult will generally be complex-'anda better` procedure is simply to,-measure--thejfinteractioml `110 length of a conductor; may beg increased by; .the

center and. decreased` bythe addition of; a large serial capacityfatithis center.; .f Y f n V e 12),

oscillators'of an arrayV to neutralize.the` elec: trmotive forcesdue tothis natural interaction bythe .introduction of couplings; between them.'

20 are, suicientlyfang-apart to A that x tancej divided. by 'the velocity "of transmissie1xV in the .ether;- ythen the' vco'ui'iling illustrated effect of the dirctfinteraction'betweenfthem I n substantially that. of radiation through?r how; by the of" indutancespthg 'enctive Wehave Considered linear; arrays and'otr'her y A v' arrays made 'upoflinear arrays inof Y i nie; extent: of. a linear array.' `-.itimryg s: es.;

an electrodynamic condition in the elemental y particles in the surface of the mirror, and these '3o. elements acting as oscillators, generate and emit kthe-reflected light. Therefore, without thinking of ,the incident light, we can think of the `reected light as due to elementary oscillatorsv lythe. surface of the mirror and operating in such phase relation that they emit a beam of light in the direction RO-Rx. Knowingy the angle of reiiection and the dimensions, the phase relation between the points and at caneasily be deduced. i

1 Without :further pursuing the illustrative case of light from a-mirror, let us turn tothe case of a linear antenna array which may be taken to be analogous tothe element 0A oi the lightv reflecting mirror shown in Fig. 24. In Fig. 25 i' we have a linear array of antennas energized accordingV to the binomial taper law andit is -desired that they shall emit a beam of maximum radiation-in the direction of the arrow B1 whose angle with Ythe normal is r. Accordingly, the "l phaserelation in the antenna units will-be given in angular measure by the expression l), arsin 1,.21rsin r, 31r sin r, etc.

In this case vthe formula for the intensityof the radiation in'any direction in the equatorial plane of `the oscillators according to the value of the angle il) willibe From this lformula it will be seen that there Vare Vtwo` other principal maximum directions as .n shown in Fig. by the arrows B2 and B3. Radiation in the direction of the arrow B3 can readily n L befannulled bysubstituting the couplet of Fig. 9 for each unit of Fig. 25 as heretofore explained in connection with Fig. 9.l Or,l the triplet' or l Fig. `11. or therquadruplet of Fig. 11a may be 'lsubstituted for each. unit of Fig. 25'.

'f By` Varying or adjusting the phase difference between consecutive unit antennas of the array of Fig.. 25, and desired'value can be given to the angle r which measures or indicates the direction, of radiation ini the beam B1. isa diagram showing the intensity of radiation in Vall horizontal directions for the array of Y Fig. 25, assuming that the angle r has the value $.45.degress. yWhen the couplet oi Fig. 9 isv suby stituted for each of the unit antennas of Fig. 3, 25, `the Ycurve is' changed from its course Ythrough fthe little circles to the courseV indicated by the "littleferosses It will be seen that the `change iis very slight'iwor thevbeams in the directions f B1 and Bz, but that the beam B3 is almost completely annulled.

radiation 'at a desired angle by adjusting' the 'phase relation among the component unit antennas may be practiced in a wide variety of i-situations. supplementing the foregoing discussionin connection with Figs. 14 to 19,l Figs. 27 andV 28 illustrate a case of power distribution Vfor anvarray'oi ve linear oscillators so as-to get vthe beams-,of radiation with their axes oblique to the `correspondingaxes of the arrays.

netic theory of light,` the incident light sets up` Fig. 2eV

`This method of kgetting a beam of maximum This is accomplished in Fig. 27 by making the nection withFig. 12, if it is desired to make the n radiation oblique, we may'proceedas in Fig. 29 in which i construct a parabola whose axis is the direction line B1 through the central antenna of the array. From the focusF ofthis parabola the lines are drawn as shown and they will v then have the proper lengthsv as power conduct-v ors from F as central station to give the maximum .of radiation in the desired direction. .Having obtained these lengths from Fig. 29, we may employ 'them in a system which departs geometrically from Fig; 29. f

As already pointed out and as is readily apparent, with a xed array of antennas the angle yoi the beam of maximum radiation can be adjusted by adjusting the phase difference; between consecutive antennas. I will point out aV case inwhich .this maybe especially useful. According to commonopinion fadingisdue to interference at the receivingI station of waves that .have been ieilected orprefracte'd Ydifferently in -relation Vto the Heaviside layer.

For example,

the transmission may loe-overA two courses as shownin Fig. -30 and the wavfes over the path designated l in that vigure may be interfered V-withand annulled at the, receiver by those over 'the path designated 2.

Changing conditions in the Beas/iside layer, such as variations -in the height of its .lower bounding'surface, Vcause the Zone 0I" kinterference on `theearths surface to vary, and this gives they well-known intermittent character of fading.r 'l

with adjustment ofthe phas'ejrelations according to the principles heretofore discussed, so that fa maximum beam of radiation will be 'given ,in

the vdirection indicated. fComparin'gfFig. JV31`with FigSO, it will be seen that the radiation from the transmitting stationy will be almost' entirely suppressed along the path' 2 of Fig.'.3,0,fand thus, in great measure, `fading at the receiving station willfbe ob'viatedQDue to changing .condi--v tions in the I-leaviside layer, the 1 angle of ele- Vationv of the maximum beam in Fig. 31 may require adjustment from time to time.. The operatorat the transmitting station willvary `this `angle until the operator at v'the''receiving station :reports to rhim that the optimum has been secured. Or, if Fig. V31 represents a receiving station, the operatorjthere will Varytheangle until he `gets ythe optimum. Y i Another case-in which an adjusted inclination `of the axis 'of the beam to the extent of the antenna array may be desirable is when wave lengths are used of the sameorder of magnitude as the ocean waves or swells. It is thenl advantageousA to direct the radio waves at an '20 In Fig. 31 a horizontalflinear,array is shown Y anglev of about 15 `degrees,'or a little less, vto

l have 'Ja 'tanere'dl linear .array ofclv2 oscillators the `earthsV surface-iwhich will produce an inf irnum transmission along' the :axis of the array,V f theconstructionmayvbefishown as in Fig. 33,v Vwhich representsfa `curtailed tapered array.- Thisg'is onthe basis of 2' 6- antennas cut/downYV Vthe Ydirection at.`ang1ev15. v I

Wave length,` this -insures jthatthe direct'beam 'Yfrm :the: array and thereflected beaumrfroml I l'1`5 the earths `surface fshallgreinforce eachA 'l other at the'angleiof 15 degreesf' n ff vAgain,v in the case of having the beam of in arr-` to 12. The binomial lc' oeflicients for- 2 6 :terms run 1, 25, 300; 2300,v 126450, 53130,'177100; 480700,

1,081,575, zetc.` fterfcrurtailmentthe ,terminal numbers becomev 480700. Dividingrtheremain-Y ing numbers through by-.4807002gives the :ooefi cientslin Fig. 33, `1 )00, 2241,42511; etc, Thev A* height,V h= 1932 )g has r'beenadjusted tov get rev` enforcement in the interference pattern *along vFig; VABAL- shows vhow thewbeams Y as --inFig. r 34'.. In both Figs 34 andg35nthe value Y* Y' ofjh'hasvbeenchosento get,reenforcernentgalong'i the preferred directionbetween'the' d ixect*andV T40 g if A 1inear :antenn a.array consistingH of a cer-` tain numberof: antennas-andfmeans tolenerg'izfeV {n.45} `them inintensitie's along`V the. array V'graded acv A cor'ding Vto the-intermediate terms-of the.5bi,l

y l fnoinial lexpansion' with a; number: of terrns'V 'great-1.'

" er than the number of; 'the antennasfA t reflected waves.

2f. vA certain number of antennas in linear atefcoefients of ,thefbin'omiali expansion'forl a. number of terms greaterrthan thefnumber of the antennas.

Y vber ofjantennasirwhich consists in 'en'ergizing'the VVso " antennas Yin Agraded lintensities corresponding to Y vnthe: interm'radiate Ycoellcientsfof the" binomial en -I` pansion for a, number offterm'sfgreater'than" the "922,115 Y graded corresponding to.` Vthe inter#V .mediate-coefllcients 1 o1'r the binornial'vk expansion for a number of Vterms-1"greater l thanV thefnumber if Y 'fdi rection.,Y :if l `at an'g1e15 may :be Vvobtained with-ga lineariarray exten'dingl horizontally In this*casethe'array-fis" on, the' basisl or-11F antennas" c zurtailedzto.v 7. flfig.A V35y t Y `shows .thesame .preferred `directionwith al vertiallyf `extendingarray tapered `and cnr-tailedv 1 alike-in respect.. togmismnl direction; ai centrar v power supply; conductor pairs therefro'ml rtogsaidj `rganterinas;VK Vthe conductors of i said Vpairs `combined' toA be non-radiative'-,V -nhase adj usters trin Vsaid conductors totgive'adesireddirectional"' ieotivity; and mean'`s tofappfortcn'energy1 toaidi. lunits'-ac'cordingtothe i'ntfierr'nediaai te'coeilcients t. of the binomial' expansion for anvexponextitfsomegl n, l ar; higher lthanflthe 'number of units inV said* v`rayand means'toenergizelthem' in gradedv infr, i tensityatzvalues corresponding tothe'fini'.'e'i'n'1vedi'-2 somewhat h herman J e; .The methgdfdfproquingigafbamgf .rgdiaf tionfromf anzfantennaarray-in a desired :direc-fr tion,` oblique `tothe direction'of extentof the' array whichlA consists 1 in :energizing theanter'ia's radiation Vinia direction fobliqg'e V tofthe-direc- Y tionfofyitsY ,rexrtentand VVmeans- 1 n antennas in intensities graded accord'ngto-,the Y coeflcients ofV a Abinomial expansion fandfat. am

properlconstanthphase difference' differingfrom zero andi-18dy degrees to give thebeamdts proben Yfnfaltnten'n'a. array consistingofa" series of reected radiation'therefrom combine with inane of transmissionV and allV said units .being oriented what series;A Y

directional jantenna units lying falong: an "airis"Y each such' unitl consistir-lgs of Ava small number volf antennasy energized7 tohave` afnull "direction fof v'transmission and 'also said units. lbeingioriented Y* anke 1n- Arespectn to, this nun direction,- -a centrar 130 e power; supply, conductora?pairsv Vtherefrnnft'o said' Y antennas;lphasej-adjusters in -saidY conductors itc@ said: series 11o `viminn :eilectl in Yardesired inclineddirection, Qeachrsuch 'unit consist-ing5.0i.-alsmall number off antennas energizedy ,tohaveagnull direction 

